本篇論文提出多蜂巢多使用者的多輸入多輸出波束成形系統下的多目標能量最小化設計。首先，我們考慮的環境是一個多蜂巢多使用者的多輸入多輸出系統，其中一個基地台同時下傳資料到多個手機端的使用者。其次，我們規劃出一個多目標最佳化問題同時最小化不同組的蜂巢傳送能量並且透過訊號對干擾雜訊比的能量限制來保持使用者的服務品質。透過間接的方法我們可以有效的找出這個多輸入多輸出波束成形系統的多目標能量最小化問題的解。接著我們透過修改後的線性矩陣不等式限制的多目標最佳化演算法以較低的複雜度來解該多目標最佳化問題。多目標基因演算法可以用來解本篇論文的多目標最佳化問題並且保證能找到一個有全域收斂性質的怕累托最佳化解集合。模擬的結果在最後呈現出來，驗證我們提出的同時最小化不同區域能量的多目標波束成形設計的效能。

In this study, we propose a multi-objective power optimization design in a multicell multiuser multiple-input multiple-output (MIMO) beamforming system. First, we consider a multicell multiuser MIMO system with multiple base station (BS), each BS serve multiple downlink mobile stations (MS) simultaneously. Second, we formulate a multi-objective optimization problem (MOP) to simultaneously minimize the downlink powers of different groups of cells with an QoS subject to a limited signal to interference plus noise ratio (SINR). An indirect method is proposed to efficiently solve the MOP of Multicell Multiuser MIMO beamforming System. Then, a LMIs-constrained multi-objective optimization algorithm is proposed to the multi-objective power minimization problem with a low computational complexity efficiently. Moreover, a novel multi-objective evolutionary algorithm (MOEA) with modification is employed for solving the MOP to guarantee the global convergence of Pareto optimal solutions. Finally, simulation results are provided to validate the performance and show the superiority of the proposed multi-objective beamforming design to minimize the downlink power of different groups of cells simultaneously.

摘要------------------------------------------------------i
Abstract-------------------------------------------------ii
誌謝----------------------------------------------------iii
Content--------------------------------------------------iv
1. Introduction------------------------------------------ 1
2. System model------------------------------------------ 3
3. Multi-objective Power Minimization Design for the Multi-
cell Multiuser MIMO Beamforming System---------------- 4
4. MOEA for Multi-objective Power minimization Beamform-
ing Design-------------------------------------------- 9
5. Multi-objective Power Minimization Beamforming Design
with sum-MSE equalization -------------------------- 10
6. Simulation Example----------------------------------- 11
7. Conclusions------------------------------------------ 21
8. Appendix--------------------------------------------- 22
References---------------------------------------------- 23

[1] Castaneda, E., Silva, A., Gameiro, A, Kountouris, M, "An Overview on Resource Allocation
Techniques for Multi-User MIMO Systems." IEEE Communications Surveys and Tutorials, pp.
239-284. 2017.
[2] Tse, D. and P. Viswanath, Fundamentals of wireless communication. 2005, Cambridge, UK ;
New York: Cam. 198-218.
[3] Paulraj, A.J., Gore, D.A. Nabar, R.U., BOLCSKEI, H., "An overview of MIMO communica-
tions - A key to gigabit wireless." Proceedings of the IEEE, vol.92, no.9, pp.198-218, 2004.
[4] Weingarten, H., Y. Steinberg, and S. Shamai, "The capacity region of the Gaussian multiple-
input multiple-output broadcast channel." IEEE Transactions on Information Theory, vol.52,
no.9, pp. 3936-3964, 2006.
[5] Agiwal, M., A. Roy, and N. Saxena, "Next Generation 5G Wireless Networks: A Comprehensive
Survey." IEEE Communications Surveys and Tutorials, vol.18, no.3, pp. 1617-1655, 2016.

[6] Shi, Q., Razaviyayn, M., Luo, Z.-Q., He, C., "An Iteratively Weighted MMSE Approach to Dis-
tributed Sum-Utility Maximization for a MIMO Interfering Broadcast Channel." IEEE Trans-
actions on Signal Processing, vol.59, no.9, pp. 4331-4340, 2011. .
[7] Nguyen, D.H.N. and L.N. Tho, "Sum-Rate Maximization in the Multicell MIMO Broadcast
Channel With Interference Coordination." IEEE Transactions on Signal Processing, vol.62, no.
6, pp. 1501-1513, 2014.
[8] Li, Y., Y.F. Tian, and C.Y. Yang, "Energy-Ecient Coordinated Beamforming Under Minimal
Data Rate Constraint of Each User." IEEE Transactions on Vehicular Technology, vol. 64, no.
6, pp. 2387-2397, 2015..
[9] Park, J., Sung, Y., Kim, D. Park, J., "Outage Probability and Outage-Based Robust Beam-
forming for MIMO Interference Channels with Imperfect Channel State Information." IEEE
Transactions on Wireless Communications, vol.11, no.10, pp. 3561-3573, 2012.
[10] Li, Y., P.Z. Fan, and N.C. Beaulieu, "Cooperative Downlink Max-Min Energy-Ecient Precod-
ing for Multicell MIMO Networks." IEEE Transactions on Vehicular Technology, vol.65, no.11,
pp. 9425-9430, 2016.
[11] Wang, X.Y. and X.D. Zhang, "Linear Transmission for Rate Optimization in MIMO Broadcast
Channels." IEEE Transactions on Wireless Communications, vol.9, no.10, pp. 3247-3257, 2010.
[12] Du, H., Ratnarajah, T., Pesavento, M., Papadias, C.B., "Joint Transceiver Beamforming in
MIMO Cognitive Radio Network Via Second-Order Cone Programming." IEEE Transactions
on Signal Processing, vol.60, no.2, pp.781-792, 2012.
[13] Zhang, Q., C. He, and L.G. Jiang, "Per-Stream MSE Based Linear Transceiver Design for
MIMO Interference Channels With CSI Error." IEEE Transactions on Communications, vol.63,
no.5,pp. 1676-1689, 2015.
[14] Shen, H. Li, B., Tao, M.Wang, X., "MSE-Based Transceiver Designs for the MIMO Interference
Channel." IEEE Transactions on Wireless Communications, vol.9, no.11, pp. 3480-3489, 2010.
[15] Xiang, Z.Z., M.X. Tao, and X.D. Wang, "Coordinated Multicast Beamforming in Multicell
Networks." IEEE Transactions on Wireless Communications, vol.12, no.1, pp. 12-21, 2013.
[16] Nguyen, D.N. and M. Krunz, "Power Minimization in MIMO Cognitive Networks using Beam-
forming Games." IEEE Journal on Selected Areas in Communications, vol.31, no.5, pp. 916-925,
2013.
[17] Codreanu, M., Tolli, A., Juntti, M. Latva-aho, M, "Joint design of tx-rx beamformers in MIMO
downlink channel." IEEE Transactions on Signal Processing, vol.55, no.9, pp. 4639-4655, 2007.
[18] Moretti, M., L. Sanguinetti, and X.D. Wang, "Resource Allocation for Power Minimization in
the Downlink of THP-Based Spatial Multiplexing MIMO-OFDMA Systems." IEEE Transac-
tions on Vehicular Technology, vol.64, no.1, pp. 405-411, 2015.
[19] Lei, L., D. Yuan, and P. Varbrand, "On Power Minimization for Non-orthogonal Multiple Access
(NOMA)." IEEE Communications Letters, vol.20, no.12, pp. 2458-2461, 2016.
[20] Ramezani-Kebrya, A., Dong, M. Liang, B. Boudreau, G. Casselman, R., "Per-Relay Power Min-
imization for Multi-user Multi-channel Cooperative Relay Beamforming." IEEE Transactions
on Wireless Communications, vol.15, no.5, pp. 3187-3198, 2016.
[21] Ng, D.W.K., Y.P.Wu, and R. Schober, "Power Ecient Resource Allocation for Full-Duplex Ra-
dio Distributed Antenna Networks." IEEE Transactions on Wireless Communications, vol.15,
no.4, pp. 2896-2911, 2016.

[22] Tabatabaee, S.M.J.A. and H. Zamiri-Jafarian, "Per-Subchannel Joint Equalizer and Receiver
Filter Design in OFDM/OQAM Systems." IEEE Transactions on Signal Processing, vol.64,
no.19, pp. 5094-5105, 2016.
[23] Li, J., D.Z. Feng, and W.X. Zheng, "Space-Time Semi-Blind Equalizer for Dispersive QAM
MIMO System Based on Modied Newton Method." IEEE Transactions on Wireless Commu-
nications, vol.13, no.6, pp. 3244-3256, 2014.
[24] Peters, S.W. and R.W. Heath, "Cooperative Algorithms for MIMO Interference Channels."
IEEE Transactions on Vehicular Technology, vol.60, no.1, pp. 206-218, 2011.
[25] Wu, H., X.Q. Gao, and X.H. You, "Robust Equalizer for Multicell Massive MIMO Uplink With
Channel Model Uncertainty." IEEE Transactions on Vehicular Technology, vol.65, no.5, pp.
3231-3242, 2016.
[26] Chiu, W.Y., H.J. Sun, and H.V. Poor, "A Multiobjective Approach to Multimicrogrid System
Design." IEEE Transactions on Smart Grid, vol.6, no.5, pp. 2263-2272, 2015.
[27] Ng, D.W.K., E.S. Lo, and R. Schober, "Multiobjective Resource Allocation for Secure Commu-
nication in Cognitive Radio Networks With Wireless Information and Power Transfer." IEEE
Transactions on Vehicular Technology, vol.65, no.5, pp. 3166-3184, 2016.
[28] Y. Sun, D. W. K. Ng, J. Zhu, and R. Schober, "Multi-Objective Optimization for Robust
Power Ecient and Secure Full-Duplex Wireless Communication Systems." IEEE Transactions
on Wireless Communications, vol.15, no.8, pp. 5511-5526, 2016.
[29] S. Leng, D. W. K. Ng, N. Zlatanov, and R. Schober, "Multi-Objective Beamforming for Energy-
Ecient SWIPT Systems." 2016 International Conference on Computing, Networking and
Communications (Icnc), 2016.
[30] S. Leng, D. W. K. Ng, N. Zlatanov, and R. Schober, "Multi-Objective Resource Allocation in
Full-Duplex SWIPT Systems." 2016 IEEE International Conference on Communications (Icc),
pp. 613-619, 2016.
[31] Chiu W.Y., Chen B.S., and H.V. Poor, "A Multiobjective Approach for Source Estimation
in Fuzzy Networked Systems." IEEE Transactions on Circuits and Systems I-Regular Papers,
vol.60, no.7, pp. 1890-1900, 2013.
[32] Chen, B.S. and Ho, S.J., "Multiobjective tracking control design of T-S fuzzy systems: Fuzzy
Pareto optimal approach." Fuzzy Sets and Systems, vol.290, pp. 39-55, 2016.
[33] Lin, C. and Chen B.S., "Achieving Pareto Optimal Power Tracking Control for Interference Lim-
ited Wireless Systems via Multi-Objective H-2/H-innity Optimization." IEEE Transactions
on Wireless Communications, vol.12, no.12, pp. 6154-6165, 2013.
[34] Xie, X.Z., H.L. Yang, and A.V. Vasilakos, "Robust Transceiver Design Based on Interference
Alignment for Multi-User Multi-Cell MIMO Networks With Channel Uncertainty." IEEE Ac-
cess, vol.5, pp. 5121-5134, 2017.
[35] Abraham, A., L.C. Jain, and R. Goldberg, "Evolutionary multiobjective optimization : theo-
retical advances and applications." Advanced information and knowledge processing. New York:
Springer. xviii, 302 p, 2005.
[36] Deb, K., "Multi-objective optimization using evolutionary algorithms. 1st ed." Wiley-
Interscience series in systems and optimization. 2001, Chichester ; New York: John Wiley
& Sons. xix, 497 p.
[37] Boyd, S.P. and L. Vandenberghe, "Convex optimization." 2004, Cambridge, UK ; New York:
Cambridge University Press. xiii, 716 p.
25
[38] Deb, K., Pratap, A., Agarwal, S., et al, "A fast and elitist multiobjective genetic algorithm:
NSGA-II." IEEE Transactions on Evolutionary Computation, vol.6, no.2, pp. 182-197, 2002.
[39] Ho, T.J. and B.S. Chen, "Robust Minimax MSE Equalizer Designs for MIMOWireless Commu-
nications With Time-Varying Channel Uncertainties." IEEE Transactions on Signal Processing,
vol.58, no.11, pp. 5835-5844, 2010.
[40] Pedersen, K.B.P.a.M.S., "The matrix cookbook." 2008: Technical University of Denmark.
[41] Jeon, Y.-S., Kim, Y.-J., Min, M., Im G, "Distributed Block Diagonalization with Selective Zero
Forcing for Multicell MU-MIMO Systems." IEEE Signal Processing Letters, vol.21, no.5, pp.
605-609, 2014.
[42] Sadek, M., A. Tarighat, and A.H. Sayed, "A leakage-based precoding scheme for downlink
multi-user MIMO channels." IEEE Transactions on Wireless Communications, vol.6, no.5, pp.
1711-1721, 2007.